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href="#对称二叉树">对称二叉树</a><ul class="sidebar-links"><li class="sidebar-link"><a class="sidebar-link-item" href="#解题代码">解题代码</a><!----></li><li class="sidebar-link"><a class="sidebar-link-item" href="#深度讲解：">深度讲解：</a><!----></li></ul></li><li class="sidebar-link"><a class="sidebar-link-item" href="#平衡二叉树">平衡二叉树</a><!----></li><!--]--></ul><!--[--><!--]--></aside><div class="sidebar-mask"></div><main class="page" data-v-7eddb2c4><div class="container" data-v-7eddb2c4><!--[--><!--]--><div style="position:relative;" class="content" data-v-7eddb2c4><div><h1 id="二叉树" tabindex="-1">二叉树 <a class="header-anchor" href="#二叉树" aria-hidden="true">#</a></h1><h2 id="二叉树递归模板" tabindex="-1">二叉树递归模板 <a class="header-anchor" href="#二叉树递归模板" aria-hidden="true">#</a></h2><p>深度遍历二叉树内的值</p><div class="language-js"><pre><code><span class="token keyword">function</span> <span class="token function">traversal</span><span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
    <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>root<span class="token punctuation">)</span><span class="token punctuation">{</span>
      console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span>
      <span class="token function">traversal</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span>
      <span class="token function">traversal</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">)</span>  
    <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre></div><h2 id="对称二叉树" tabindex="-1">对称二叉树 <a class="header-anchor" href="#对称二叉树" aria-hidden="true">#</a></h2><p>力扣101题</p><p>给你一个二叉树的根节点 root ， 检查它是否轴对称。</p><p><img src="https://assets.leetcode.com/uploads/2021/02/19/symtree1.jpg" alt="图片"></p><div class="language-js"><pre><code>输入：root <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">]</span>
输出：<span class="token boolean">true</span>
</code></pre></div><h3 id="解题代码" tabindex="-1">解题代码 <a class="header-anchor" href="#解题代码" aria-hidden="true">#</a></h3><div class="language-js"><pre><code><span class="token keyword">var</span> <span class="token function-variable function">isSymmetric</span> <span class="token operator">=</span> <span class="token keyword">function</span> <span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">==</span> <span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token keyword">return</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>
  <span class="token keyword">return</span> <span class="token function">dfs</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">,</span> root<span class="token punctuation">.</span>right<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>

<span class="token keyword">function</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token parameter">root1<span class="token punctuation">,</span> root2</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token keyword">if</span> <span class="token punctuation">(</span>root1 <span class="token operator">==</span> <span class="token keyword">null</span> <span class="token operator">&amp;&amp;</span> root2 <span class="token operator">==</span> <span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>  <span class="token comment">// 如果此时两个子树都为空，说明已经对称，返回true</span>
    <span class="token keyword">return</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>
  <span class="token keyword">if</span> <span class="token punctuation">(</span>root1 <span class="token operator">==</span> <span class="token keyword">null</span> <span class="token operator">||</span> root2 <span class="token operator">==</span> <span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>  <span class="token comment">// 如果两个节点只有一个为空，说明不对称，返回false</span>
    <span class="token keyword">return</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>
  <span class="token keyword">if</span> <span class="token punctuation">(</span>root1<span class="token punctuation">.</span>val <span class="token operator">!=</span> root2<span class="token punctuation">.</span>val<span class="token punctuation">)</span> <span class="token punctuation">{</span>  <span class="token comment">// 如果两个节点的值不相同，说明不对称，返回false</span>
    <span class="token keyword">return</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>
  <span class="token comment">// dfs left节点的左子树 和 right节点的右子树，left节点的右子树 和 right节点的左子树</span>
  <span class="token keyword">return</span> <span class="token function">dfs</span><span class="token punctuation">(</span>root1<span class="token punctuation">.</span>left<span class="token punctuation">,</span> root2<span class="token punctuation">.</span>right<span class="token punctuation">)</span> <span class="token operator">&amp;&amp;</span> <span class="token function">dfs</span><span class="token punctuation">(</span>root1<span class="token punctuation">.</span>right<span class="token punctuation">,</span> root2<span class="token punctuation">.</span>left<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</code></pre></div><p>这道题是一个树的遍历问题，考验对于递归的理解和应用。其主要思路是通过遍历树的左右子树，比较它们的节点值，判断是否对称。</p><p>代码中，isSymmetric方法首先判断根结点是否为空，若为空则返回true，否则调用dfs()方法比较所有左右节点的值。在dfs()方法中，首先判断两个节点是否都为空（即到了叶子节点），若为空则说明该子树对称，返回true。若有一个为空，说明该子树不对称，返回false。然后判断两节点的值是否相同，若不同，说明不对称，返回false。最后递归比较左节点的左子树和右节点的右子树，以及左节点的右子树和右节点的左子树，若对称则返回true，否则返回false。</p><p>该方法递归的过程中，不断比较每一个左右节点的值，直至到达叶子节点或者节点不对称。若每个节点都对称，则该树对称，返回true，否则返回false。</p><p>总的来说，该题的解题思路是通过树的遍历以及递归，比较当前节点的左右子树是否对称，最终返回一个布尔值表示是否对称。</p><h3 id="深度讲解：" tabindex="-1">深度讲解： <a class="header-anchor" href="#深度讲解：" aria-hidden="true">#</a></h3><p>return dfs(root1.left, root2.right) &amp;&amp; dfs(root1.right, root2.left);</p><p>这一行代码的含义是判断当前节点的左右子树是否对称，根据题目可知，对称的定义是：每个节点的左子树和右子树进行镜像对称时相等。因此，要同时比较两组子节点（root1的左节点与root2的右节点，root1的右节点与root2的左节点），而不是只比较一组子节点。</p><p>如果只写 dfs(root1.left, root2.right)，则只比较了root1的左节点与root2的右节点的对称性，没考虑到另一组子节点的对称性，会导致最终判断结果出现问题。例如下面的二叉树：</p><pre><code> 1
</code></pre><p>/ <br> 2 2 / \ / <br> 3 4 4 3</p><p>如果只比较 dfs(root1.left, root2.right)，则在比较到左右子树节点 2 和 2 时，return的是 true，但是比较到节点 4 和 4 时，return 的是 false，然后就会得到错误的结果，虽然它们的左右子树都是相同的，但不是对称的。</p><p>因此，需要同时比较两组子节点，用 &amp;&amp; 连接表示两个结果都为 true，树才是对称的</p><h2 id="平衡二叉树" tabindex="-1">平衡二叉树 <a class="header-anchor" href="#平衡二叉树" aria-hidden="true">#</a></h2><p>力扣110题</p><p>借助二叉树最大深度的递归函数，进行解题</p><div class="language-js"><pre><code><span class="token keyword">var</span> <span class="token function-variable function">isBalanced</span> <span class="token operator">=</span> <span class="token keyword">function</span> <span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">==</span> <span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>
    <span class="token comment">//返回深度</span>
    <span class="token keyword">let</span> left <span class="token operator">=</span> <span class="token function">maxDepth</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token keyword">let</span> right <span class="token operator">=</span> <span class="token function">maxDepth</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token keyword">if</span> <span class="token punctuation">(</span>Math<span class="token punctuation">.</span><span class="token function">abs</span><span class="token punctuation">(</span>left <span class="token operator">-</span> right<span class="token punctuation">)</span> <span class="token operator">&gt;</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>
    <span class="token keyword">return</span> <span class="token function">isBalanced</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">)</span> <span class="token operator">&amp;&amp;</span> <span class="token function">isBalanced</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span><span class="token punctuation">;</span>


<span class="token punctuation">}</span><span class="token punctuation">;</span>

<span class="token keyword">var</span> <span class="token function-variable function">maxDepth</span> <span class="token operator">=</span> <span class="token keyword">function</span> <span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token comment">// 如果根节点为空，返回 0 表示深度为 0</span>
    <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">===</span> <span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>
    <span class="token comment">// 递归地计算左子树的最大深度</span>
    <span class="token keyword">const</span> leftMax <span class="token operator">=</span> <span class="token function">maxDepth</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token comment">// 递归地计算右子树的最大深度</span>
    <span class="token keyword">const</span> rightMax <span class="token operator">=</span> <span class="token function">maxDepth</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token comment">// 根据左右子树的最大深度推出原二叉树的最大深度</span>
    <span class="token comment">// 该节点的深度是其左右子树深度的最大值再加上 1</span>
    <span class="token comment">// 1 表示该节点本身的深度也要计入</span>
    <span class="token keyword">return</span> <span class="token number">1</span> <span class="token operator">+</span> Math<span class="token punctuation">.</span><span class="token function">max</span><span class="token punctuation">(</span>leftMax<span class="token punctuation">,</span> rightMax<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>
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